Theorem baibr 872

Description: Move conjunction outside of biconditional. (Contributed by NM, 11-Jul-1994.)

Hypothesis

Ref	Expression
baib.1	|- (ph <-> (ps /\ ch))

Assertion

Ref	Expression
baibr	|- (ps -> (ch <-> ph))

Proof of Theorem baibr

Step	Hyp	Ref	Expression
1		baib.1	. . 3 |- (ph <-> (ps /\ ch))
2	1	baib 871	. 2 |- (ps -> (ph <-> ch))
3	2	bicomd 192	1 |- (ps -> (ch <-> ph))

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  rbaibr  874  pm5.44  877  exmoeu2  2247  ssnelpss  3613  brinxp  4836